Prove that the distinct equivalence classes of the relation of congruence modulo n are the sets , where for each , .
To prove that the distinct equivalence classes of the relation of congruence modulo are the sets .
where for each
Let us suppose is the positive integer which is divided by , so now using the Euclid’s division lemma, the following equation can be written −
So from the above equation the possible remainders when is divided by will be .
Now let us construct the equivalence classes of the above remainders which can be
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